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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, WORK, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.3.1) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * -- April 2011 -- 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER UPLO 00010 INTEGER INFO, N 00011 * .. 00012 * .. Array Arguments .. 00013 INTEGER IPIV( * ) 00014 COMPLEX*16 AP( * ), WORK( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * ZSPTRI computes the inverse of a complex symmetric indefinite matrix 00021 * A in packed storage using the factorization A = U*D*U**T or 00022 * A = L*D*L**T computed by ZSPTRF. 00023 * 00024 * Arguments 00025 * ========= 00026 * 00027 * UPLO (input) CHARACTER*1 00028 * Specifies whether the details of the factorization are stored 00029 * as an upper or lower triangular matrix. 00030 * = 'U': Upper triangular, form is A = U*D*U**T; 00031 * = 'L': Lower triangular, form is A = L*D*L**T. 00032 * 00033 * N (input) INTEGER 00034 * The order of the matrix A. N >= 0. 00035 * 00036 * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) 00037 * On entry, the block diagonal matrix D and the multipliers 00038 * used to obtain the factor U or L as computed by ZSPTRF, 00039 * stored as a packed triangular matrix. 00040 * 00041 * On exit, if INFO = 0, the (symmetric) inverse of the original 00042 * matrix, stored as a packed triangular matrix. The j-th column 00043 * of inv(A) is stored in the array AP as follows: 00044 * if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; 00045 * if UPLO = 'L', 00046 * AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. 00047 * 00048 * IPIV (input) INTEGER array, dimension (N) 00049 * Details of the interchanges and the block structure of D 00050 * as determined by ZSPTRF. 00051 * 00052 * WORK (workspace) COMPLEX*16 array, dimension (N) 00053 * 00054 * INFO (output) INTEGER 00055 * = 0: successful exit 00056 * < 0: if INFO = -i, the i-th argument had an illegal value 00057 * > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its 00058 * inverse could not be computed. 00059 * 00060 * ===================================================================== 00061 * 00062 * .. Parameters .. 00063 COMPLEX*16 ONE, ZERO 00064 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), 00065 $ ZERO = ( 0.0D+0, 0.0D+0 ) ) 00066 * .. 00067 * .. Local Scalars .. 00068 LOGICAL UPPER 00069 INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP 00070 COMPLEX*16 AK, AKKP1, AKP1, D, T, TEMP 00071 * .. 00072 * .. External Functions .. 00073 LOGICAL LSAME 00074 COMPLEX*16 ZDOTU 00075 EXTERNAL LSAME, ZDOTU 00076 * .. 00077 * .. External Subroutines .. 00078 EXTERNAL XERBLA, ZCOPY, ZSPMV, ZSWAP 00079 * .. 00080 * .. Intrinsic Functions .. 00081 INTRINSIC ABS 00082 * .. 00083 * .. Executable Statements .. 00084 * 00085 * Test the input parameters. 00086 * 00087 INFO = 0 00088 UPPER = LSAME( UPLO, 'U' ) 00089 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00090 INFO = -1 00091 ELSE IF( N.LT.0 ) THEN 00092 INFO = -2 00093 END IF 00094 IF( INFO.NE.0 ) THEN 00095 CALL XERBLA( 'ZSPTRI', -INFO ) 00096 RETURN 00097 END IF 00098 * 00099 * Quick return if possible 00100 * 00101 IF( N.EQ.0 ) 00102 $ RETURN 00103 * 00104 * Check that the diagonal matrix D is nonsingular. 00105 * 00106 IF( UPPER ) THEN 00107 * 00108 * Upper triangular storage: examine D from bottom to top 00109 * 00110 KP = N*( N+1 ) / 2 00111 DO 10 INFO = N, 1, -1 00112 IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO ) 00113 $ RETURN 00114 KP = KP - INFO 00115 10 CONTINUE 00116 ELSE 00117 * 00118 * Lower triangular storage: examine D from top to bottom. 00119 * 00120 KP = 1 00121 DO 20 INFO = 1, N 00122 IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO ) 00123 $ RETURN 00124 KP = KP + N - INFO + 1 00125 20 CONTINUE 00126 END IF 00127 INFO = 0 00128 * 00129 IF( UPPER ) THEN 00130 * 00131 * Compute inv(A) from the factorization A = U*D*U**T. 00132 * 00133 * K is the main loop index, increasing from 1 to N in steps of 00134 * 1 or 2, depending on the size of the diagonal blocks. 00135 * 00136 K = 1 00137 KC = 1 00138 30 CONTINUE 00139 * 00140 * If K > N, exit from loop. 00141 * 00142 IF( K.GT.N ) 00143 $ GO TO 50 00144 * 00145 KCNEXT = KC + K 00146 IF( IPIV( K ).GT.0 ) THEN 00147 * 00148 * 1 x 1 diagonal block 00149 * 00150 * Invert the diagonal block. 00151 * 00152 AP( KC+K-1 ) = ONE / AP( KC+K-1 ) 00153 * 00154 * Compute column K of the inverse. 00155 * 00156 IF( K.GT.1 ) THEN 00157 CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 ) 00158 CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ), 00159 $ 1 ) 00160 AP( KC+K-1 ) = AP( KC+K-1 ) - 00161 $ ZDOTU( K-1, WORK, 1, AP( KC ), 1 ) 00162 END IF 00163 KSTEP = 1 00164 ELSE 00165 * 00166 * 2 x 2 diagonal block 00167 * 00168 * Invert the diagonal block. 00169 * 00170 T = AP( KCNEXT+K-1 ) 00171 AK = AP( KC+K-1 ) / T 00172 AKP1 = AP( KCNEXT+K ) / T 00173 AKKP1 = AP( KCNEXT+K-1 ) / T 00174 D = T*( AK*AKP1-ONE ) 00175 AP( KC+K-1 ) = AKP1 / D 00176 AP( KCNEXT+K ) = AK / D 00177 AP( KCNEXT+K-1 ) = -AKKP1 / D 00178 * 00179 * Compute columns K and K+1 of the inverse. 00180 * 00181 IF( K.GT.1 ) THEN 00182 CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 ) 00183 CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ), 00184 $ 1 ) 00185 AP( KC+K-1 ) = AP( KC+K-1 ) - 00186 $ ZDOTU( K-1, WORK, 1, AP( KC ), 1 ) 00187 AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) - 00188 $ ZDOTU( K-1, AP( KC ), 1, AP( KCNEXT ), 00189 $ 1 ) 00190 CALL ZCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 ) 00191 CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, 00192 $ AP( KCNEXT ), 1 ) 00193 AP( KCNEXT+K ) = AP( KCNEXT+K ) - 00194 $ ZDOTU( K-1, WORK, 1, AP( KCNEXT ), 1 ) 00195 END IF 00196 KSTEP = 2 00197 KCNEXT = KCNEXT + K + 1 00198 END IF 00199 * 00200 KP = ABS( IPIV( K ) ) 00201 IF( KP.NE.K ) THEN 00202 * 00203 * Interchange rows and columns K and KP in the leading 00204 * submatrix A(1:k+1,1:k+1) 00205 * 00206 KPC = ( KP-1 )*KP / 2 + 1 00207 CALL ZSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 ) 00208 KX = KPC + KP - 1 00209 DO 40 J = KP + 1, K - 1 00210 KX = KX + J - 1 00211 TEMP = AP( KC+J-1 ) 00212 AP( KC+J-1 ) = AP( KX ) 00213 AP( KX ) = TEMP 00214 40 CONTINUE 00215 TEMP = AP( KC+K-1 ) 00216 AP( KC+K-1 ) = AP( KPC+KP-1 ) 00217 AP( KPC+KP-1 ) = TEMP 00218 IF( KSTEP.EQ.2 ) THEN 00219 TEMP = AP( KC+K+K-1 ) 00220 AP( KC+K+K-1 ) = AP( KC+K+KP-1 ) 00221 AP( KC+K+KP-1 ) = TEMP 00222 END IF 00223 END IF 00224 * 00225 K = K + KSTEP 00226 KC = KCNEXT 00227 GO TO 30 00228 50 CONTINUE 00229 * 00230 ELSE 00231 * 00232 * Compute inv(A) from the factorization A = L*D*L**T. 00233 * 00234 * K is the main loop index, increasing from 1 to N in steps of 00235 * 1 or 2, depending on the size of the diagonal blocks. 00236 * 00237 NPP = N*( N+1 ) / 2 00238 K = N 00239 KC = NPP 00240 60 CONTINUE 00241 * 00242 * If K < 1, exit from loop. 00243 * 00244 IF( K.LT.1 ) 00245 $ GO TO 80 00246 * 00247 KCNEXT = KC - ( N-K+2 ) 00248 IF( IPIV( K ).GT.0 ) THEN 00249 * 00250 * 1 x 1 diagonal block 00251 * 00252 * Invert the diagonal block. 00253 * 00254 AP( KC ) = ONE / AP( KC ) 00255 * 00256 * Compute column K of the inverse. 00257 * 00258 IF( K.LT.N ) THEN 00259 CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 00260 CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+N-K+1 ), WORK, 1, 00261 $ ZERO, AP( KC+1 ), 1 ) 00262 AP( KC ) = AP( KC ) - ZDOTU( N-K, WORK, 1, AP( KC+1 ), 00263 $ 1 ) 00264 END IF 00265 KSTEP = 1 00266 ELSE 00267 * 00268 * 2 x 2 diagonal block 00269 * 00270 * Invert the diagonal block. 00271 * 00272 T = AP( KCNEXT+1 ) 00273 AK = AP( KCNEXT ) / T 00274 AKP1 = AP( KC ) / T 00275 AKKP1 = AP( KCNEXT+1 ) / T 00276 D = T*( AK*AKP1-ONE ) 00277 AP( KCNEXT ) = AKP1 / D 00278 AP( KC ) = AK / D 00279 AP( KCNEXT+1 ) = -AKKP1 / D 00280 * 00281 * Compute columns K-1 and K of the inverse. 00282 * 00283 IF( K.LT.N ) THEN 00284 CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 00285 CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1, 00286 $ ZERO, AP( KC+1 ), 1 ) 00287 AP( KC ) = AP( KC ) - ZDOTU( N-K, WORK, 1, AP( KC+1 ), 00288 $ 1 ) 00289 AP( KCNEXT+1 ) = AP( KCNEXT+1 ) - 00290 $ ZDOTU( N-K, AP( KC+1 ), 1, 00291 $ AP( KCNEXT+2 ), 1 ) 00292 CALL ZCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 ) 00293 CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1, 00294 $ ZERO, AP( KCNEXT+2 ), 1 ) 00295 AP( KCNEXT ) = AP( KCNEXT ) - 00296 $ ZDOTU( N-K, WORK, 1, AP( KCNEXT+2 ), 1 ) 00297 END IF 00298 KSTEP = 2 00299 KCNEXT = KCNEXT - ( N-K+3 ) 00300 END IF 00301 * 00302 KP = ABS( IPIV( K ) ) 00303 IF( KP.NE.K ) THEN 00304 * 00305 * Interchange rows and columns K and KP in the trailing 00306 * submatrix A(k-1:n,k-1:n) 00307 * 00308 KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1 00309 IF( KP.LT.N ) 00310 $ CALL ZSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 ) 00311 KX = KC + KP - K 00312 DO 70 J = K + 1, KP - 1 00313 KX = KX + N - J + 1 00314 TEMP = AP( KC+J-K ) 00315 AP( KC+J-K ) = AP( KX ) 00316 AP( KX ) = TEMP 00317 70 CONTINUE 00318 TEMP = AP( KC ) 00319 AP( KC ) = AP( KPC ) 00320 AP( KPC ) = TEMP 00321 IF( KSTEP.EQ.2 ) THEN 00322 TEMP = AP( KC-N+K-1 ) 00323 AP( KC-N+K-1 ) = AP( KC-N+KP-1 ) 00324 AP( KC-N+KP-1 ) = TEMP 00325 END IF 00326 END IF 00327 * 00328 K = K - KSTEP 00329 KC = KCNEXT 00330 GO TO 60 00331 80 CONTINUE 00332 END IF 00333 * 00334 RETURN 00335 * 00336 * End of ZSPTRI 00337 * 00338 END
1.7.3 
